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Lévy processes and infinitely divisible distributions
TLDR
In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.Abstract:
Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.read more
Citations
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BookDOI
Fluctuations of Lévy Processes with Applications
TL;DR: In this article, Kloeden, P., Ombach, J., Cyganowski, S., Kostrikin, A. J., Reddy, J.A., Pokrovskii, A., Shafarevich, I.A.
Journal ArticleDOI
Ten equivalent definitions of the fractional laplace operator
TL;DR: In this article, several definitions of the Riesz fractional Laplace operator in R^d have been studied, including singular integrals, semigroups of operators, Bochner's subordination, and harmonic extensions.
Journal ArticleDOI
Optimal stopping and perpetual options for Lévy processes
TL;DR: A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formulas for perpetual American put options involving the infimum of the after-mentioned process are obtained.
Journal ArticleDOI
Density and tails of unimodal convolution semigroups
TL;DR: For the isotropic unimodal probability convolutional semigroups, this article gave sharp bounds for their Levy-Khintchine exponent with Matuszewska indices strictly between 0 and 2.
Extreme Events: Dynamics, Statistics and Prediction
TL;DR: In this paper, the authors review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics.
References
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Journal ArticleDOI
Two-step estimation of ergodic Lévy driven SDE
Hiroki Masuda,Yuma Uehara +1 more
TL;DR: In this paper, the authors consider high frequency samples from ergodic Levy driven stochastic differential equation with drift coefficient and scale coefficient, and prove the joint asymptotic normality of estimators of a class of functional parameters, which are constructed in a two-step manner: first, they use the Gaussian quasi-likelihood for estimation of the functional parameters and then, for estimating the drift coefficient, they make use of the method of moments based on the Euler-type residual.
Posted Content
Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders
Soobin Cho,Panki Kim +1 more
TL;DR: In this paper, the transition densities of subordinators whose Levy measures are continuous and decaying in a mixed polynomial order were investigated under a weaker assumption on Levy measures, and they also obtained a precise asymptotic behavior at infinity.
DissertationDOI
Infinitely divisible and related distributions and Lévy driven stochastic partial differential equations
TL;DR: In this paper, the authors studied the class of quasi-infinitely divisible distributions and Lévy driven stochastic partial differential equations and obtained bounds of the integral modulus of continuity in terms of the characteristic triplet.
Journal ArticleDOI
Domains of attraction for positive and discrete tempered stable distributions
TL;DR: In this paper, the authors introduce a large and flexible class of discrete tempered stable distributions, and analyze the domains of attraction for both this class and the related class of positive tempered stable distribution.